Problem: Express your answer as a mixed number simplified to lowest terms. $11\dfrac{2}{4}-3\dfrac{9}{15} = {?}$
Solution: Simplify each fraction. $= {11\dfrac{1}{2}} - {3\dfrac{3}{5}}$ Find a common denominator for the fractions: $= {11\dfrac{5}{10}}-{3\dfrac{6}{10}}$ Convert ${11\dfrac{5}{10}}$ to ${10 + \dfrac{10}{10} + \dfrac{5}{10}}$ So the problem becomes: ${10\dfrac{15}{10}}-{3\dfrac{6}{10}}$ Separate the whole numbers from the fractional parts: $= {10} + {\dfrac{15}{10}} - {3} - {\dfrac{6}{10}}$ Bring the whole numbers together and the fractions together: $= {10} - {3} + {\dfrac{15}{10}} - {\dfrac{6}{10}}$ Subtract the whole numbers: $=7 + {\dfrac{15}{10}} - {\dfrac{6}{10}}$ Subtract the fractions: $= 7+\dfrac{9}{10}$ Combine the whole and fractional parts into a mixed number: $= 7\dfrac{9}{10}$